3.1580 \(\int \frac{1}{(1-2 x)^2 (2+3 x) (3+5 x)} \, dx\)

Optimal. Leaf size=42 \[ \frac{2}{77 (1-2 x)}-\frac{136 \log (1-2 x)}{5929}-\frac{9}{49} \log (3 x+2)+\frac{25}{121} \log (5 x+3) \]

[Out]

2/(77*(1 - 2*x)) - (136*Log[1 - 2*x])/5929 - (9*Log[2 + 3*x])/49 + (25*Log[3 + 5
*x])/121

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Rubi [A]  time = 0.050606, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{2}{77 (1-2 x)}-\frac{136 \log (1-2 x)}{5929}-\frac{9}{49} \log (3 x+2)+\frac{25}{121} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)),x]

[Out]

2/(77*(1 - 2*x)) - (136*Log[1 - 2*x])/5929 - (9*Log[2 + 3*x])/49 + (25*Log[3 + 5
*x])/121

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Rubi in Sympy [A]  time = 7.48448, size = 36, normalized size = 0.86 \[ - \frac{136 \log{\left (- 2 x + 1 \right )}}{5929} - \frac{9 \log{\left (3 x + 2 \right )}}{49} + \frac{25 \log{\left (5 x + 3 \right )}}{121} + \frac{2}{77 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(1-2*x)**2/(2+3*x)/(3+5*x),x)

[Out]

-136*log(-2*x + 1)/5929 - 9*log(3*x + 2)/49 + 25*log(5*x + 3)/121 + 2/(77*(-2*x
+ 1))

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Mathematica [A]  time = 0.0498303, size = 40, normalized size = 0.95 \[ \frac{\frac{154}{1-2 x}-136 \log (3-6 x)-1089 \log (3 x+2)+1225 \log (-3 (5 x+3))}{5929} \]

Antiderivative was successfully verified.

[In]  Integrate[1/((1 - 2*x)^2*(2 + 3*x)*(3 + 5*x)),x]

[Out]

(154/(1 - 2*x) - 136*Log[3 - 6*x] - 1089*Log[2 + 3*x] + 1225*Log[-3*(3 + 5*x)])/
5929

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Maple [A]  time = 0.013, size = 35, normalized size = 0.8 \[{\frac{25\,\ln \left ( 3+5\,x \right ) }{121}}-{\frac{9\,\ln \left ( 2+3\,x \right ) }{49}}-{\frac{2}{-77+154\,x}}-{\frac{136\,\ln \left ( -1+2\,x \right ) }{5929}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1-2*x)^2/(2+3*x)/(3+5*x),x)

[Out]

25/121*ln(3+5*x)-9/49*ln(2+3*x)-2/77/(-1+2*x)-136/5929*ln(-1+2*x)

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Maxima [A]  time = 1.332, size = 46, normalized size = 1.1 \[ -\frac{2}{77 \,{\left (2 \, x - 1\right )}} + \frac{25}{121} \, \log \left (5 \, x + 3\right ) - \frac{9}{49} \, \log \left (3 \, x + 2\right ) - \frac{136}{5929} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((5*x + 3)*(3*x + 2)*(2*x - 1)^2),x, algorithm="maxima")

[Out]

-2/77/(2*x - 1) + 25/121*log(5*x + 3) - 9/49*log(3*x + 2) - 136/5929*log(2*x - 1
)

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Fricas [A]  time = 0.22913, size = 68, normalized size = 1.62 \[ \frac{1225 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) - 1089 \,{\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) - 136 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 154}{5929 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((5*x + 3)*(3*x + 2)*(2*x - 1)^2),x, algorithm="fricas")

[Out]

1/5929*(1225*(2*x - 1)*log(5*x + 3) - 1089*(2*x - 1)*log(3*x + 2) - 136*(2*x - 1
)*log(2*x - 1) - 154)/(2*x - 1)

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Sympy [A]  time = 0.400493, size = 36, normalized size = 0.86 \[ - \frac{136 \log{\left (x - \frac{1}{2} \right )}}{5929} + \frac{25 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{9 \log{\left (x + \frac{2}{3} \right )}}{49} - \frac{2}{154 x - 77} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(1-2*x)**2/(2+3*x)/(3+5*x),x)

[Out]

-136*log(x - 1/2)/5929 + 25*log(x + 3/5)/121 - 9*log(x + 2/3)/49 - 2/(154*x - 77
)

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GIAC/XCAS [A]  time = 0.208974, size = 54, normalized size = 1.29 \[ -\frac{2}{77 \,{\left (2 \, x - 1\right )}} - \frac{9}{49} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) + \frac{25}{121} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((5*x + 3)*(3*x + 2)*(2*x - 1)^2),x, algorithm="giac")

[Out]

-2/77/(2*x - 1) - 9/49*ln(abs(-7/(2*x - 1) - 3)) + 25/121*ln(abs(-11/(2*x - 1) -
5))